esc_html would be used inside of html for example between a <p> tag

<p><?php echo esc_html( $some_variable ); ?></p>

esc_attr would be used for escaping attribute values on html tags like so:

<p my-attribute="<?php echo esc_attr( $some_variable ); ?>"></p>

applying _e to the end will automatically echo it for you e.g:

<p><?php esc_html_e( $some_variable ); ?></p>

<p my-attribute="<?php esc_attr_e( $some_variable ); ?>"></p>

esc_html would be used inside of html for example between a <p> tag

<p><?php echo esc_html( $some_variable ); ?></p>

esc_attr would be used for escaping attribute values on html tags like so:

<p my-attribute="<?php echo esc_attr( $some_variable ); ?>"></p>

applying _e to the end is for using it with text domains and will automatically echo it for you e.g:

<p><?php esc_html_e( 'some-text', 'text-domain' ); ?></p>

<p my-attribute="<?php esc_attr_e( 'some-text', 'text-domain' ); ?>"></p>

in addition to _e there is also __ which does the same as _e but doesnt echo it so you can store it in a variable.